Generalized Biot-Willis parameters

Equation (a11) has already determined the coefficient a₁₁. Thus, (Kutwop) shows that  

$$a_{12} + a_{13} = - {{1/K^*-1/K_u}\over{B}} = - \alpha/K^*.$$ (23)

This relation provides a constraint on the sum of the two generalized Biot-Willis parameters for the double-porosity problem.

Not all of these long-time results are independent. In fact, there are only three independent equations among the five given above expressing the a_ij in terms of the single-porosity (long-time) moduli.